Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term

Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term Full article

Conference

IX Международная конференция, посвященная 120-летию со дня рождения академика Михаила Алексеевича Лаврентьева, «Лаврентьевские чтения по математике, механике и физике»
07-11 Sep 2020 , Новосибирск

Journal

Journal of Physics: Conference Series
ISSN: 1742-6588

Output data

Year: 2020, Volume: 1666, Article number : 012025, Pages count : 6 DOI: 10.1088/1742-6596/1666/1/012025

Authors

Kuznetsov I V ^1,2 , Sazhenkov S A ^1,2

Affiliations

1	Novosibirsk State University
2	Lavrentyev Institute of Hydrodynamics SB RAS

Funding (1)

Министерство науки и высшего образования Российской Федерации

FWGG-2021-0010

The Cauchy-Dirichlet problem for the genuinely nonlinear ultra-parabolic equation with the piece-wise smooth minor term is considered. The minor term depends on a small positive parameter and collapses to the one-sided Dirac delta function as this parameter tends to zero. As the result, we arrive at the limiting initial-boundary value problem for the impulsive ultra-parabolic equation. The peculiarity is that the standard entropy solution of the problem for the impulsive equation generally is not unique. In this report, we propose a rule for selecting the `proper' entropy solution, relying on the limiting procedure in the original problem incorporating the smooth minor term.

Kuznetsov I.V. , Sazhenkov S.A.
Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term
Journal of Physics: Conference Series. 2020. V.1666. 012025 :1-6. DOI: 10.1088/1742-6596/1666/1/012025 Scopus РИНЦ OpenAlex

Scopus:	2-s2.0-85097094374
Elibrary:	45138083
OpenAlex:	W3110571853

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